Arithmetic-Geometric Progressions & Mixed Series

Grade 11 Maths — Arithmetic-Geometric Progressions & Mixed Series: 25 practice questions with instant scoring and explanations.

1. An arithmetic-geometric progression combines:
2. The series 1 + 2x + 3x² + 4x³ + ... is:
3. For the AGP series S = 1 + 2x + 3x² + ... with |x| < 1, sum is:
4. The series 1·2 + 2·2² + 3·2³ + ... is:
5. Sum of AGP a + (a+d)r + (a+2d)r² + ... (|r| < 1) is:
6. The series 1 + 3/2 + 5/4 + 7/8 + ... is:
7. Find sum of 1 + 2(1/2) + 3(1/2)² + ... (infinite):
8. The sum of first n terms of AGP depends on:
9. For AGP 1·1 + 2·(1/2) + 3·(1/4) + ..., sum to infinity is:
10. The series 1/2 + 2/4 + 3/8 + ... is:
11. For the series S_n = 1 + 2x + 3x² + 4x³ + ... + nx^(n-1), the sum is:
12. In the series 1 + 2r + 3r² + 4r³ + ..., if r = 1/3, sum to infinity is:
13. The terms of an AGP are coefficients of which expansion?
14. For AGP with first term a=2, common difference d=1, common ratio r=1/2, first three terms are:
15. The formula S = a/(1-r) + dr/(1-r)² applies when:
16. The series 1 + 4x + 9x² + 16x³ + ... is:
17. Sum of 1·2 + 2·3 + 3·4 + ... + n(n+1) is:
18. For the series S = 1 + 2(1/3) + 3(1/3)² + ..., sum is:
19. The sum 1·1 + 2·2 + 3·3 + ... + n·n = ?
20. A mixed series means:
21. Sum of 1·2² + 2·3² + 3·4² + ... + n(n+1)² is:
22. The series 1 + (1+2) + (1+2+3) + ... is:
23. For convergence of AGP S = Σ(a+nd)r^n, we need:
24. Sum of 1 + 2/2 + 3/4 + 4/8 + ... (infinite) is:
25. For AGP starting with 'a', difference 'd', ratio 'r', nth term is: